Scale dependence of local f_NL

TL;DR

This work analyzes the scale dependence of the local non-Gaussianity parameter $f_{-}{ m NL}$ in both multi-field local and single-field quasi-local inflationary models using the $\delta N$ formalism. It derives compact expressions for the running $n_{f_{NL}}$ in a range of setups, revealing that scale dependence is typically first order in slow-roll and can arise from differential scale behavior of multiple Gaussian fields or from non-linear evolution after horizon exit. The results show that mixed inflaton-curvaton and multi-curvaton scenarios generally produce a nonzero $n_{f_{NL}}$, while pure quadratic single-field models may yield zero running; observational prospects depend on how large $f_{ m NL}$ is near current bounds. Overall, the paper provides a unified framework to quantify and compare the scale dependence of local-type non-Gaussianity across diverse inflationary models, with implications for Planck and large-scale structure analyses.

Abstract

We consider possible scale-dependence of the non-linearity parameter f_NL in local and quasi-local models of non-Gaussian primordial density perturbations. In the simplest model where the primordial perturbations are a quadratic local function of a single Gaussian field then f_NL is scale-independent by construction. However scale-dependence can arise due to either a local function of more than one Gaussian field, or due to non-linear evolution of modes after horizon-exit during inflation. We show that the scale dependence of f_NL is typically first order in slow-roll. For some models this may be observable with experiments such as Planck provided that f_NL is close to the current observational bounds.

Figures (1)

• Figure 1: An estimate for the function $f(s)$ in equation (\ref{['curvaton_nnl_quartic']}) shown as a log-linear plot. For $s\lesssim 1$ only a qualitative agreement (error $\sim20\%$) with the exact behaviour is expected.